Preface.

References.

Acknowledgments.

**1. Introduction.**

1.1 Introduction.

1.2 Bayesian Signal Processing.

1.3 Simulation-Based Approach to Bayesian Processing.

1.4 Bayesian Model-Based Signal Processing.

1.5 Notation and Terminology.

References.

Problems.

**2. Bayesian Estimation.**

2.1 Introduction.

2.2 Batch Bayesian Estimation.

2.3 Batch Maximum Likelihood Estimation.

2.4 Batch Minimum Variance Estimation.

2.5 Sequential Bayesian Estimation.

2.6 Summary.

References.

Problems.

**3. Simulation-Based Bayesian Methods.**

3.1 Introduction.

3.2 Probability Density Function Estimation.

3.3 Sampling Theory.

3.4 Monte Carlo Approach.

3.5 Importance Sampling.

3.6 Sequential Importance Sampling.

3.7 Summary.

References.

Problems.

**4. State-Space Models for Bayesian Processing.**

4.1 Introduction.

4.2 Continuous-Time State-Space Models.

4.3 Sampled-Data State-Space Models.

4.4 Discrete-Time State-Space Models.

4.5 Gauss-Markov State-Space Models.

4.6 Innovations Model.

4.7 State-Space Model Structures.

4.8 Nonlinear (Approximate) Gauss-Markov State-Space Models.

4.9 Summary.

References.

Problems.

**5. Classical Bayesian State-Space Processors.**

5.1 Introduction.

5.2 Bayesian Approach to the State-Space.

5.3 Linear Bayesian Processor (Linear Kalman Filter).

5.4 Linearized Bayesian Processor (Linearized Kalman Filter).

5.5 Extended Bayesian Processor (Extended Kalman Filter).

5.6 Iterated-Extended Bayesian Processor (Iterated-Extended Kalman Filter).

5.7 Practical Aspects of Classical Bayesian Processors.

5.8 Case Study: RLC Circuit Problem.

5.9 Summary.

References.

Problems.

**6. Modern Bayesian State-Space Processors.**

6.1 Introduction.

6.2 Sigma-Point (Unscented) Transformations.

6.3 Sigma-Point Bayesian Processor (Unscented Kalman Filter).

6.4 Quadrature Bayesian Processors.

6.5 Gaussian Sum (Mixture) Bayesian Processors.

6.6 Case Study: 2D-Tracking Problem.

6.7 Summary.

References.

Problems.

**7. Particle-Based Bayesian State-Space Processors.**

7.1 Introduction.

7.2 Bayesian State-Space Particle Filters.

7.3 Importance Proposal Distributions.

7.4 Resampling.

7.5 State-Space Particle Filtering Techniques.

7.6 Practical Aspects of Particle Filter Design.

7.7 Case Study: Population Growth Problem.

7.8 Summary.

References.

Problems.

**8. Joint Bayesian State/Parametric Processors.**

8.1 Introduction.

8.2 Bayesian Approach to Joint State/Parameter Estimation.

8.3 Classical/Modern Joint Bayesian State/Parametric Processors.

8.3.1 Classical Joint Bayesian Processor.

8.3.2 Modern Joint Bayesian Processor.

8.4 Particle-Based Joint Bayesian State/Parametric Processors.

8.5 Case Study: Random Target Tracking using a Synthetic Aperture Towed Array.

8.6 Summary.

References.

Problems.

**9. Discrete Hidden Markov Model Bayesian Processors.**

9.1 Introduction.

9.2 Hidden Markov Models.

9.3 Properties of the Hidden Markov Model.

9.4 HMM Observation Probability: Evaluation Problem.

9.5 State Estimation in HMM: The Viterbi Technique.

9.6 Parameter Estimation in HMM: The EM/Baum-Welch Technique.

9.7 Case Study: Time-Reversal Decoding.

9.8 Summary.

References.

Problems.

**10. Bayesian Processors for Physics-Based Applications.**

10.1 Optimal Position Estimation for the Automatic Alignment.

10.2 Broadband Ocean Acoustic Processing.

10.3 Bayesian Processing for Biothreats.

10.4 Bayesian Processing for the Detection of Radioactive Sources.

References.

Appendix A. Probability & Statistics Overview.

A.1 Probability Theory.

A.2 Gaussian Random Vectors.

A.3 Uncorrelated Transformation: Gaussian Random Vectors.

Referencess.